# Realizability Interpretation and Normalization of Typed Call-by-Need $λ$-calculus With Control

1 GALLINETTE - GALLINETTE
Inria Rennes – Bretagne Atlantique , LS2N - Laboratoire des Sciences du Numérique de Nantes
2 PI.R2 - Design, study and implementation of languages for proofs and programs
PPS - Preuves, Programmes et Systèmes, UPD7 - Université Paris Diderot - Paris 7, CNRS - Centre National de la Recherche Scientifique, Inria de Paris
Abstract : We define a variant of realizability where realizers are pairs of a term and a substitution. This variant allows us to prove the normalization of a simply-typed call-by-need $λ-$calculus with control due to Ariola et al. Indeed, in such call-by-need calculus, substitutions have to be delayed until knowing if an argument is really needed. In a second step, we extend the proof to a call-by-need $λ$-calculus equipped with a type system equivalent to classical second-order predicate logic, representing one step towards proving the normalization of the call-by-need classical second-order arithmetic introduced by the second author to provide a proof-as-program interpretation of the axiom of dependent choice.
Type de document :
Communication dans un congrès
FOSSACS 18, 2018, Thessalonique, Greece
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https://hal.inria.fr/hal-01624839
Contributeur : Étienne Miquey <>
Soumis le : vendredi 2 mars 2018 - 16:38:31
Dernière modification le : mardi 6 mars 2018 - 12:45:54

### Identifiants

• HAL Id : hal-01624839, version 2
• ARXIV : 1803.00914

### Citation

Étienne Miquey, Hugo Herbelin. Realizability Interpretation and Normalization of Typed Call-by-Need $λ$-calculus With Control. FOSSACS 18, 2018, Thessalonique, Greece. 〈hal-01624839v2〉

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